Abstract
An optimal control method for seismic-excited building structures with multiple time delays is investigated in this paper. The system state equation with multiple time delays is discretized and transformed into a standard discrete form without any explicit time delay by a particular augmenting for state variables. A time-delay controller is then designed based on this standard equation using the discrete optimal control method. Effectiveness of the proposed controller is demonstrated by numerical simulations. Simulation results indicate that a very small time delay may result in the instability of the control system if it is not compensated in the control design. Time delay may be compensated effectively by the proposed controller, in the mean time, an effective control may be obtained. The proposed controller is valid for both small and large time delays.
Similar content being viewed by others
References
Hu, H Y. On dynamics in vibration with time delay (in Chinese). Chinese Journal of Vibration Engineering 10(3), 273–279 (1997)
Abdel-Rohman, M. Time-delay effects on active damped structures. Journal of Engineering Mechanics, ASCE 113(11), 1709–1719 (1987)
Chung, L. L., Reinhorn, A. M., and Soong, T. T. Experiments on active control of seismic structures. Journal of Engineering Mechanics, ASCE 114(2), 241–256 (1988)
McGreery, S., Soong, T. T., and Reinhorn, A. M. An experiments study of time delay compensation in active structural control. Proceeding of 6th International Modal Analysis Conference, SEM, 1733–1739 (1988)
Cai, G. P. and Huang, J. Z. Optimal control method for seismically excited building structures with time-delay in control. Journal of Engineering Mechanics, ASCE 128(6), 602–612 (2002)
Xu, J. and Chung, K. W. Effects of time delayed position feedback on a van der Pol-Duffing oscillator. Physica D 18(1–2), 17–39 (2003)
Hosek, M. and Olgac, N. A single-step automatic tuning algorithm for the delayed resonator vibration absorber. IEEE/ASME Transactions on Mechatronics 7(2), 245–255 (2002)
Chen, L. X. Delayed Feedback Control and Experiment Study of Flexible Structures (in Chinese), Ph. D. dissertation, Shanghai Jiaotong University (2008)
Cai, G. P. and Lim, C. W. Optimal tracking control of flexible hub-beam system with time delay. Multibody System Dynamics 16(4), 331–350 (2006)
Wang, Z. H. and Hu, H. Y. Stabilization of vibration systems via delayed state difference feedback. Journal of Sound and Vibration 296(1–2), 117–129 (2006)
Sun, Z. Q. Theory and Application of Computer Control (in Chinese), Tsinghua University Press, Beijing (1989)
Yang, J. N., Wu, J. C., Reinhorn, A. M., and Riley, M. Control of sliding-isolated buildings using sliding-mode control. Journal of Structural Engineering 122(2), 179–186 (1996)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Li-qun CHEN
Project supported by the National Natural Science Foundation of China (Nos. 10772112, 10472065), the Key Project of Ministry of Education of China (No. 107043), the Key Scientific Project of Shanghai Municipal Education Commission (No. 09ZZ17), the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20070248032), and the Research Project of State Key Laboratory of Ocean Engineering of China (No. GKZD010807)
Rights and permissions
About this article
Cite this article
Chen, Lx., Cai, Gp. Design method of multiple time-delay controller for active structural vibration control. Appl. Math. Mech.-Engl. Ed. 30, 1405–1414 (2009). https://doi.org/10.1007/s10483-009-1106-z
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10483-009-1106-z